It's no secret to anyone how important it is to know the multiplication and division tables, in particular when performing arithmetic calculations and solving math examples.
However, what if the child is frightened by this huge set of numbers, called the " Multiplication and division table", And knowing it by heart seems to be a completely impossible task?
Then we hasten to calm down - Learning the whole multiplication table is very easy! To do this, you need to remember only 36 combinations of numbers (bundles of three numbers). Here we do not take into account the multiplication by 1 and 10, since this is an elementary action that does not require much effort in memorization.
Description of the online simulator
This simulator works on the basis of a specially developed algorithm for increasing the complexity of examples: starting with the simplest numbers “2 x 2”, gradually increasing the complexity to “9 x 9”. Thus smoothly luring into the learning process.
Thus, you will have to memorize the multiplication table in small portions, which will significantly reduce the load, since children will direct their attention to just a few examples, forgetting about the entire “large” volume.
The Simulator has a settings menu for selecting the table study mode. It is possible to select an action - "Multiplication" or "Division", a range of examples "Entire table" or "By some number". All this is an extended functionality of the site and is available after payment.
Each new example is accompanied by help hint, so it will be easier for the child to start his study and memorize new combinations unknown to him.
If, in the course of training, any example causes difficulty, you can quickly remind yourself of its result using additional clue, this will help you more effectively cope with remembering difficult examples.
Percentage scale will quickly let you know what level of knowledge of the multiplication table you have.
An example is considered fully learned if the correct answer was given 4 times in a row. However, upon reaching 100% , we urge you not to quit studying, but to return the next day and refresh your knowledge by going through all the examples again. After all, it is regular classes that develop memory and strengthen skills!
Description of the online simulator interface
Firstly, the simulator has a "quick access panel", which includes 4 buttons. They allow you to: go to the main page of the site, enable or disable sound signals, reset learning results (start studying again), and also get to the reviews and comments page.
Secondly, it is the main structure of the program.
Above all is percentage scale, showing the approximate level of knowledge of the multiplication table.
Below comes example field that needs to be answered. During the answer, it will change its color: it will turn red - if an incorrect answer was given, green - in case of a correct one, blue - after using the hint, and yellowish - while showing a new example.
Next is message line. It displays textual information about errors, correct answers, as well as help and additional tips.
At the end is screen keyboard, containing only the buttons necessary for work: all the numbers, "backspace" - if you need to correct the answer, the "Check" and "Additional hint" buttons.
We are sure that this simulator "Multiplication Table in 20 minutes" will help.
And multiplication. Just about the operation of multiplication and will be discussed in this article.
Number multiplication
Multiplication of numbers is mastered by children in the second grade, and there is nothing complicated about it. Now we will look at multiplication by examples.
Example 2*5. This means either 2+2+2+2+2 or 5+5. We take 5 two times or 2 five times. The answer is 10 respectively.
Example 4*3. Similarly, 4+4+4 or 3+3+3+3. Three times 4 or four times 3. Answer 12.
Example 5*3. We do the same as the previous examples. 5+5+5 or 3+3+3+3+3. Answer 15.
Multiplication formulas
Multiplication is the sum of identical numbers, for example, 2 * 5 = 2 + 2 + 2 + 2 + 2 or 2 * 5 = 5 + 5. The multiplication formula is:
Where, a is any number, n is the number of terms a. Let's say a=2, then 2+2+2=6, then n=3 multiplying 3 by 2, we get 6. Consider in reverse order. For example, given: 3 * 3, that is. 3 multiplied by 3 - this means that the three must be taken 3 times: 3 + 3 + 3 \u003d 9. 3 * 3 \u003d 9.
Abbreviated multiplication
Abbreviated multiplication is an abbreviation of the multiplication operation in certain cases, and formulas for abbreviated multiplication have been developed specifically for this. Which will help to make the calculations the most rational and fast:
Abbreviated multiplication formulas
Let a, b belong to R, then:
The square of the sum of two expressions is the square of the first expression plus twice the product of the first expression and the second plus the square of the second expression. Formula: (a+b)^2 = a^2 + 2ab + b^2
The square of the difference of two expressions is the square of the first expression minus twice the product of the first expression and the second plus the square of the second expression. Formula: (a-b)^2 = a^2 - 2ab + b^2
Difference of squares two expressions is equal to the product of the difference of these expressions and their sum. Formula: a^2 - b^2 = (a - b)(a + b)
sum cube of two expressions is equal to the cube of the first expression plus three times the square of the first expression times the second plus three times the product of the first expression times the square of the second plus the cube of the second expression. Formula: (a + b)^3 = a^3 + 3a(^2)b + 3ab^2 + b^3
difference cube of two expressions is equal to the cube of the first expression minus three times the product of the square of the first expression and the second plus three times the product of the first expression and the square of the second minus the cube of the second expression. Formula: (a-b)^3 = a^3 - 3a(^2)b + 3ab^2 - b^3
Sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of cubes two expressions is equal to the product of the sum of the first and second expressions by the incomplete square of the difference of these expressions. Formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Sign up for the course "Speed up mental counting, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. In 30 days, you will learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.
Multiplication of fractions
Considering the addition and subtraction of fractions, the rule was voiced, bringing fractions to a common denominator in order to perform the calculation. When multiplying this do No need! When multiplying two fractions, the denominator is multiplied by the denominator and the numerator by the numerator.
For example, (2/5) * (3 * 4). Multiply two thirds by one quarter. We multiply the denominator by the denominator, and the numerator by the numerator: (2 * 3) / (5 * 4), then 6/20, we make a reduction, we get 3/10.
Multiplication Grade 2
The second grade is just the beginning of learning multiplication, so second graders solve the simplest tasks to replace addition with multiplication, multiply numbers, learn the multiplication table. Let's look at multiplication tasks at the second grade level:
Oleg lives in a five-story building, on the top floor. The height of one floor is 2 meters. What is the height of the house?
The box contains 10 packs of biscuits. Each pack contains 7 pieces. How many cookies are in the box?
Misha arranged his toy cars in a row. There are 7 of them in each row, and there are only 8 rows. How many cars does Misha have?
There are 6 tables in the dining room, and 5 chairs are pushed behind each table. How many chairs are in the dining room?
Mom brought 3 bags of oranges from the store. The packages contain 22 oranges. How many oranges did mom bring?
There are 9 strawberry bushes growing in the garden, and 11 berries grow on each bush. How many berries grow on all the bushes?
Roma put 8 pipe parts one after the other, the same size of 2 meters. What is the length of the full pipe?
Parents brought their children to school on the first of September. 12 cars arrived, each with 2 children. How many children did their parents bring in these cars?
Multiplication Grade 3
In the third grade, more serious tasks are given. In addition to multiplication, division will also be passed.
Among the tasks for multiplication will be: multiplication of two-digit numbers, multiplication by a column, replacement of addition by multiplication and vice versa.
Column multiplication:
Column multiplication is the easiest way to multiply large numbers. Consider this method using the example of two numbers 427 * 36.
1 step. Let's write the numbers one under the other, so that 427 is at the top and 36 is at the bottom, that is, 6 under 7, 3 under 2.
2 step. We start multiplication with the rightmost digit of the bottom number. That is, the order of multiplication is: 6 * 7, 6 * 2, 6 * 4, then the same with the triple: 3 * 7, 3 * 2, 3 * 4.
So, first multiply 6 by 7, the answer is: 42. We write it down like this: since it turned out 42, then 4 are tens, and 2 are ones, the recording is similar to addition, which means we write 2 under the six, and 4 is added to the two of the number 427.
3 step. Then we do the same with 6 * 2. Answer: 12. The first ten, which is added to the four of the number 427, and the second - units. We add the resulting two with the four from the previous multiplication.
4 step. Multiply 6 by 4. The answer is 24 and add 1 from the previous multiplication. We get 25.
So, multiplying 427 by 6, the answer is 2562
REMEMBER! The result of the second multiplication should be written down under SECOND number of the first result!
5 step. We perform similar actions with the number 3. We get the multiplication answer 427 * 3 = 1281
6 step. Then we add the received answers when multiplying and get the final answer of the multiplication 427 * 36. Answer: 15372.
Multiplication Grade 4
The fourth class is the multiplication of only large numbers. The calculation is performed by the multiplication method in a column. The method is described above in an accessible language.
For example, find the product of the following pairs of numbers:
- 988 * 98 =
- 99 * 114 =
- 17 * 174 =
- 164 * 19 =
Multiplication Presentation
Download a presentation on multiplication with the simplest tasks for second graders. The presentation will help children navigate this operation better, because it is presented in a colorful and playful way - in the best way for a child to learn!
Multiplication table
The multiplication table is studied by every student in the second grade. Everyone must know it!
Sign up for the course "Speed up mental counting, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. In 30 days, you will learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.
Multiplication Examples
Multiplication by unambiguous
- 9 * 5 =
- 9 * 8 =
- 8 * 4 =
- 3 * 9 =
- 7 * 4 =
- 9 * 5 =
- 8 * 8 =
- 6 * 9 =
- 6 * 7 =
- 9 * 2 =
- 8 * 5 =
- 3 * 6 =
Multiplication by two digits
- 4 * 16 =
- 11 * 6 =
- 24 * 3 =
- 9 * 19 =
- 16 * 8 =
- 27 * 5 =
- 4 * 31 =
- 17 * 5 =
- 28 * 2 =
- 12 * 9 =
Two-digit multiplication by two-digit
- 24 * 16 =
- 14 * 17 =
- 19 * 31 =
- 18 * 18 =
- 10 * 15 =
- 15 * 40 =
- 31 * 27 =
- 23 * 25 =
- 17 * 13 =
Multiplication of three-digit numbers
- 630 * 50 =
- 123 * 8 =
- 201 * 18 =
- 282 * 72 =
- 96 * 660 =
- 910 * 7 =
- 428 * 37 =
- 920 * 14 =
Games for the development of mental counting
Special educational games developed with the participation of Russian scientists from Skolkovo will help improve oral counting skills in an interesting game form.
Game "Quick Score"
The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer "yes" or "no" to the question "are there 5 identical fruits?". Follow your goal, and this game will help you with this.
Game "Mathematical matrices"
"Mathematical Matrices" great brain exercise for kids, which will help you develop his mental work, mental counting, quick search for the right components, attentiveness. The essence of the game is that the player has to find a pair from the proposed 16 numbers that will give a given number in total, for example, in the picture below, this number is “29”, and the desired pair is “5” and “24”.
Game "Numerical coverage"
The game "number coverage" will load your memory while practicing with this exercise.
The essence of the game is to remember the number, which takes about three seconds to memorize. Then you need to play it. As you progress through the stages of the game, the number of numbers grows, start with two and go on.
Game "Guess the operation"
The game "Guess the operation" develops thinking and memory. The main essence of the game is to choose a mathematical sign so that the equality is true. Examples are given on the screen, look carefully and put the desired “+” or “-” sign so that the equality is true. The sign "+" and "-" are located at the bottom of the picture, select the desired sign and click on the desired button. If you answer correctly, you score points and continue playing.
Game "Simplify"
The game "Simplify" develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.
Game "Fast Addition"
The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers, the sum of which is equal to a given number. This game is given a matrix from one to sixteen. A given number is written above the matrix, you must select the numbers in the matrix so that the sum of these numbers is equal to the given number. If you answer correctly, you score points and continue playing.
Game "Visual Geometry"
The game "Visual Geometry" develops thinking and memory. The main essence of the game is to quickly count the number of shaded objects and select it from the list of answers. In this game, blue squares are shown on the screen for a few seconds, they must be quickly counted, then they close. Four numbers are written below the table, you must select one correct number and click on it with the mouse. If you answer correctly, you score points and continue playing.
Game "Mathematical Comparisons"
The game "Mathematical Comparisons" develops thinking and memory. The main essence of the game is to compare numbers and mathematical operations. In this game, you have to compare two numbers. At the top, a question is written, read it and answer correctly to the question posed. You can answer using the buttons below. There are three buttons "left", "equal" and "right". If you answer correctly, you score points and continue playing.
Development of phenomenal mental arithmetic
We have considered only the tip of the iceberg, in order to understand mathematics better - sign up for our course: Speeding up mental counting.
From the course, you will not only learn dozens of tricks for simplified and fast multiplication, addition, multiplication, division, calculating percentages, but also work them out in special tasks and educational games! Mental counting also requires a lot of attention and concentration, which are actively trained in solving interesting problems.
Speed reading in 30 days
Increase your reading speed by 2-3 times in 30 days. From 150-200 to 300-600 wpm or from 400 to 800-1200 wpm. The course uses traditional exercises for the development of speed reading, techniques that speed up the work of the brain, a method for progressively increasing the speed of reading, understands the psychology of speed reading and the questions of course participants. Suitable for children and adults reading up to 5,000 words per minute.
The secrets of brain fitness, we train memory, attention, thinking, counting
The brain, like the body, needs exercise. Physical exercise strengthens the body, mental exercise develops the brain. 30 days of useful exercises and educational games for the development of memory, concentration, intelligence and speed reading will strengthen the brain, turning it into a tough nut to crack.
Money and the mindset of a millionaire
Why are there money problems? In this course, we will answer this question in detail, look deep into the problem, consider our relationship with money from a psychological, economic and emotional point of view. From the course, you will learn what you need to do to solve all your financial problems, start saving money and invest it in the future.
Knowing the psychology of money and how to work with them makes a person a millionaire. 80% of people with an increase in income take out more loans, becoming even poorer. Self-made millionaires, on the other hand, will make millions again in 3-5 years if they start from scratch. This course teaches the proper distribution of income and cost reduction, motivates you to learn and achieve goals, teaches you to invest money and recognize a scam.
Topic: Multiplication table and division by 2. (Consolidation lesson)
Purpose: to consolidate the computational skills of the multiplication and division tables.
Lesson objectives:
1. Consolidate knowledge of the multiplication and division tables; develop the ability to solve complex problems; keep building your computing skills.
2. Develop logical and economic thinking; the ability to draw conclusions, to generalize.
3. Working in groups, cultivate such personality traits as cooperation, mutual assistance, tolerance; respect for work and people of work.
Lesson type : a lesson in improving and consolidating skills.
During the classes.
1. Organizational moment. Psychological mood of students.
The bell rang, class began.
- Guys,imagine that your palms are a small mirror, look into it, smile at yourself - you see how cute and smart you are! Look at each other, smile, and your mood will be cheerful and upbeat, you will want to learn new things, because it's so interesting!
There was a wise man who knew everything. One man decided to prove that the wise man does not know everything. Clutching the butterfly in his palms, he asked: “Tell me, sage, which butterfly is in my hands: dead or alive?” And he himself thinks: “If the living one says, I will kill her, if the dead one says, I will release her.” The sage, thinking, replied: "Everything is in your hands."
Your knowledge is also in your hands. Let's prove it with our work in the lesson.
(Slide 1)
II. Updating of basic knowledge.
To work quickly and dexterously
We need training for the mind.
a) What is the odd number?(Slide 2)
What task do you need to do with numbers? (Remove extra number)
7 14 21 27 28 35 42 49
5 10 11 15 20 25 30 35
4 8 12 16 17 20 24 28
What did you need to know to complete the task? (Multiplication tables)
Evaluation.
b) Say the word.
I invite you to ask questions about the topic of today's lesson.
1. An action that can replace the sum of identical terms (multiplication)
2. Number to be divided by (divisor)
3. The number that is divided (dividend)
4. The result of the action during multiplication (product)
5. Result of action when dividing (quotient)
6. Multiplication action component (multiplier)
Slide 3. Evaluation.
III. Independent formulation of the topic and purpose of the lesson. Target setting for the lesson.
Who guessed what the topic of the lesson is?
Multiplication and division table.
Guys, what is our goal?
slide 4
Today we will consolidate knowledge of the multiplication and division tables, we will use the table to solve problems, equations, and find the value of an expression.
Problem question.
What do you think, is it possible, by repeating and consolidating, to learn something new? We need to figure it out.
4. Mental account
1. Statement of the problem. Mystery.
To find out what will be discussed today, you will need to guess the Russian folk riddle “There is a bunch of piglets, whoever touches them will squeal”. Doubt the answer? And now we will solve this problem by performing calculations.
slide 5
What's in front of us? (block diagram)
How will we do the calculations? (by algorithm)
What is an algorithm? (perform actions in order)
Recorded numbers 13, 4, 8, 17, 5 write in ascending order (4, 5, 8, 13, 17)
slide 6
What word came out? (bees)
What else will we talk about in class?
Evaluation.
Slide 7
Guys, bees are tireless workers. And the branch of agriculture is beekeeping. What is this industry doing? (by breeding bees)
A person of what profession is breeding bees? (beekeeper).
Guys, do you have a beekeeper in your village?
Do you think he knows everything about bees? (Yes)
The main thing in this profession is that the beekeeper must know everything about bees.
What do you know about bees?
Unfortunately, we cannot know everything about bees, but we will try to find out as much as possible. I'm sure you will succeed.
Today one of the bees will accompany us in the lesson. So, on the way to the bee.
Work in pairs. Finding the value of expressions with variables.
- Our road starts from the hive. There are usually many beehives in the apiary. Each hive has its own entrance - notch. In order to open the notch, we need to complete the task. What is our goal with this task? (execute variable expressions) -What is an expression with a variable?
| c:2 |
| C*2 |
Evaluation. Mutual testing and self-testing according to the standard.
Slide 8
You know the multiplication and division tables very well, the notch in the hives is open and it is no coincidence that our hives turned out to be just such colors. (Yellow, blue, white). The bee simply does not distinguish other colors. But on the other hand, she sees ultraviolet rays, which are not subject to our eyes.
IV. Logic task.
Do you know how many eyes a bee has? (No)
Let's verbally count.
A bee has as many eyes as you have, as many again, and half as many more. (A bee has 5 eyes. 2 large ones, consisting in turn of 10 thousand eyes, and located on the sides of the head and 3 small ones on the forehead between them)
V. Work on consolidating the material covered.
1. Mathematical dictation. Work in notebooks.
Beekeepers usually assign their own numbers to the hives in the apiary. There are such numbers in our apiary. “But we will know them when we complete the task. Write down only the answers.
1) Product of numbers 2 and 4
2) Increase 2 by 9 times
3) How many times is 14 greater than 2
4) 1 multiplier 2, the second is the same. Work?
5) Reduce 20 by 2 times
6) What number was reduced by 2 times if you got 5
7) How much did you multiply 8 if you got 16
Slide 9
8 18 7 4 10 10 2
Evaluation. Cross-checking from the slide.
2. Speech about bees. (Ruban Vanya.)
Hello guys! I am a worker bee. We produce wax, propolis, the most valuable medicine - honey and bee bread. Perga is bee bread made from pollen and nectar. We eat it, the bees.
What do you know about the bee family? (The main thing in the bee family is the queen - she is the queen. The rest of the bees are workers. They perform the work of watchmen, cell cleaners, fans, nectar collectors, cell builders. Drones live with them, who do nothing, but are needed for procreation.)
3. Writing expressions and finding their values. Slide 10
It's time for the bee to go to work. What time does the student work day start? (8 hours) How do you tell time? (by hours)
The bee is well oriented in time. For this, she does not need a watch or the sun. She needs flowers. She takes off whenthe flower clock begins to work.
How do you understand my words?
So we will work with colors and find the meanings of expressions. The first number in the mathematical expression shows the time when the flower “wakes up”, the answer you found is when it “falls asleep”.
What is important to know in order to complete this task? (procedure)
Rosehip 2*7-10:2=
Poppy 5+ 7*2 - 11=
Evaluation. Mutual verification.
4. The task of finding the perimeter of a rectangle. slide 11
What do we see on the slide? (frame)
Why does a beekeeper need it?
What kind of work can we do? (find the sides and perimeter of the rectangle).
S - 12 dm2
Length - 3 dm
What formulas helped?
Formulas for finding the perimeter, area.
What else helped?
Multiplication and division table.
5. differentiated work.
Work according to textbook No. 2 (strong students) Peer review.
Work on cards (weak students) Self-examination.
5. Work on the task. (Cards)
Bees are such hard workers! And we will solve the problem for them.
Read the problem, there are several solutions to it. You need to choose one correct solution, mark it with a plus. Explain your choice.
Task . Uncle Vitya pumped out 7 kg of honey from one hive, and 2 times more from the other. How many kg of honey did Uncle Vitya pump out from two beehives?
slide 12
VII. Summary of the lesson.
Our lesson is coming to an end. At the beginning of the lesson, I asked you if it was possible to learn something new in the repetition and consolidation lesson. What conclusion did you come to?
What new did you learn in the lesson? (the industry is beekeeping, the profession is a beekeeper. The more bees fly to work, the more harvest we will collect, the more beautiful our Earth will be from fragrant flowers.) - What did you study?
Our bee thanks you for your work.
Did you enjoy collaborating, working in pairs, collectively?
You also worked like bees today, and I really enjoyed working with you.
This page contains examples describing multiplication by 2 and multiplication of 2, division, some ways of writing and pronunciation, a multiplication table by 2 without answers, at the end of the article there are pictures for download with which you can print the multiplication and division by 2 table.
Multiply by 2:
1 x 2 = 2
2 x 2 = 4
3 x 2 = 6
4 x 2 = 8
5 x 2 = 10
6 x 2 = 12
7 x 2 = 14
8 x 2 = 16
9 x 2 = 18
10 x 2 = 20
First pronunciation:
1 x 2 = 2 (1 times 2 equals 2)
2 x 2 = 4 (2 times 2 equals 4)
3 x 2 = 6 (3 times 2 equals 6)
4 x 2 = 8 (4 times 2 equals 8)
5 x 2 = 10 (5 times 2 equals 10)
6 x 2 = 12 (6 times 2 equals 12)
7 x 2 = 14 (7 times 2 equals 14)
8 x 2 = 16 (8 times 2 equals 16)
9 x 2 = 18 (9 times 2 equals 18)
10 x 2 = 20 (10 times 2 equals 20)
Second pronunciation:
1 x 2 \u003d 2 (take 1 2 times, you get 2)
2 x 2 \u003d 4 (take 2 2 times, you get 4)
3 x 2 = 6 (take 3 2 times, you get 6)
4 x 2 \u003d 8 (take 4 2 times, you get 8)
5 x 2 \u003d 10 (take 5 2 times, you get 10)
6 x 2 \u003d 12 (take 6 2 times, you get 12)
7 x 2 \u003d 14 (take 7 2 times, you get 14)
8 x 2 \u003d 16 (take 2 times 8, you get 16)
9 x 2 \u003d 18 (take 9 2 times, you get 18)
10 x 2 \u003d 20 (take 10 2 times, you get 20)
Sometimes it is also pronounced like this:
2 ∙ 2 = 4 (twice two is four)
The value of the product does not change from changing the places of the factors, therefore, knowing the results of multiplication by 2, you can easily find the results of multiplying the number 2. Different symbols are used as a multiplication sign in different sources. An example with (x) was shown above, this time we will write using a raised dot (∙)
Multiplying the number 2:
2 ∙ 1 = 2
2 ∙ 2 = 4
2 ∙ 3 = 6
2 ∙ 4 = 8
2 ∙ 5 = 10
2 ∙ 6 = 12
2 ∙ 7 = 14
2 ∙ 8 = 16
2 ∙ 9 = 18
2 ∙ 10 = 20
Pronunciation options:
2 ∙ 1 \u003d 2 (take 2 1 time, you get 2)
2 ∙ 2 \u003d 4 (take 2 2 times, you get 4)
2 ∙ 3 \u003d 6 (take 2 3 times, you get 6)
2 ∙ 4 \u003d 8 (take 2 4 times, you get 8)
2 ∙ 5 = 10 (take 2 5 times, you get 10)
2 ∙ 6 \u003d 12 (take 2 6 times, you get 12)
2 ∙ 7 \u003d 14 (take 2 7 times, you get 14)
2 ∙ 8 = 16 (take 2 8 times, you get 16)
2 ∙ 9 \u003d 18 (take 2 9 times, you get 18)
2 ∙ 10 \u003d 20 (take 2 10 times, you get 20)
2 ∙ 1 = 2 (2 times 1 equals 2)
2 ∙ 2 = 4 (2 times 2 equals 4)
2 ∙ 3 = 6 (2 times 3 equals 6)
2 ∙ 4 = 8 (2 times 4 equals 8)
2 ∙ 5 = 10 (2 times 5 equals 10)
2 ∙ 6 = 12 (2 times 6 equals 12)
2 ∙ 7 = 14 (2 times 7 equals 14)
2 ∙ 8 = 16 (2 times 8 equals 16)
2 ∙ 9 = 18 (2 times 9 equals 18)
2 ∙ 10 = 20 (2 times 10 equals 20)
Division by 2:
2 ÷ 2 = 1 (2 divided by 2 equals 1)
4 ÷ 2 = 2 (4 divided by 2 equals 2)
6 ÷ 2 = 3 (6 divided by 2 equals 3)
8 ÷ 2 = 4 (8 divided by 2 equals 4)
10 ÷ 2 = 5 (10 divided by 2 equals 5)
12 ÷ 2 = 6 (12 divided by 2 equals 6)
14 ÷ 2 = 7 (14 divided by 2 equals 7)
16 ÷ 2 = 8 (16 divided by 2 equals 8)
18 ÷ 2 = 9 (18 divided by 2 equals 9)
20 ÷ 2 = 10 (20 divided by 2 equals 10)
Picture:
Division. Picture:
Multiplication and division table by 2 without answers (in order and randomly):
| 1 ∙ 2 = | 7 ∙ 2 = | 2 ÷ 2 = | 10 ÷ 2 = |
| 2 ∙ 2 = | 8 ∙ 2 = | 4 ÷ 2 = | 2 ÷ 2 = |
| 3 ∙ 2 = | 9 ∙ 2 = | 6 ÷ 2 = | 4 ÷ 2 = |
| 4 ∙ 2 = | 10 ∙ 2 = | 8 ÷ 2 = | 6 ÷ 2 = |
| 5 ∙ 2 = | 1 ∙ 2 = | 10 ÷ 2 = | 8 ÷ 2 = |
| 6 ∙ 2 = | 2 ∙ 2 = | 12 ÷ 2 = | 16 ÷ 2 = |
| 7 ∙ 2 = | 3 ∙ 2 = | 14 ÷ 2 = | 18 ÷ 2 = |
| 8 ∙ 2 = | 4 ∙ 2 = | 16 ÷ 2 = | 12 ÷ 2 = |
| 9 ∙ 2 = | 5 ∙ 2 = | 18 ÷ 2 = | 14 ÷ 2 = |
| 10 ∙ 2 = | 6 ∙ 2 = | 20 ÷ 2 = | 4 ÷ 2 = |
This part of the table is usually, if not the first, then one of the first in the study. We have already talked about ways to write, now consider an example with multiplication by 2, connect old knowledge with new
Here 5 is the first factor, 2 is the second factor, and 10 is the value of the product
Often, a raised dot (5 ∙ 2) and an “asterisk” or “snowflake” (5 * 2) are also used as a multiplication sign, and other designations can be found.
We have already said in the main part that if we write down the multiplication table for numbers from 1 to 10, then we can see that when the places of the factors change, the value of the product does not change (based on this, the commutative multiplication law is formulated), so you can learn only half multiplication tables and, knowing it, quickly find answers for the remaining half. By the way, there are other ways to quickly learn a table, as well as ways to quickly count without memorizing a table.
So, we just said that multiplying the number 2 by 5 gives the same number as multiplying 5 by 2:
5 x 2 = 2 x 5 = 10.
But here you need to be very careful when it comes to not just numbers, but to specific tasks and examples. Many textbooks recommend using the first factor to indicate what is being added, and using the second to indicate how many times.
Let's take the following situation as an example: Vasya and Petya were going to draw. Mom gave everyone 5 sheets of paper, which means there will be 10 sheets in total. This can be written in the usual way using the plus sign (5 + 5 = 10), or it can be written using two multipliers and a multiplication sign.
Based on the fact that each factor plays a certain role during recording, we can conclude that if the value of the product does not change due to a change in the places of the factors, this does not mean that you can always write the factors in any order. Heated disputes periodically flare up about the order of recording multipliers, we hope that mutual understanding will be reached on this issue soon. To understand the logic of recommendations about the order of factors, it is necessary to draw a parallel with the already known addition again, in fact, with the above method of writing, the first factor shows which number to add (in our case 5), and the second - how many such numbers need to be added, t i.e. the entry "5 x 2" indicates that you need to take five sheets twice. In any case, it is important to understand the meaning of what is written on paper.
The question may also arise: why is such a record needed at all? Why introduce a new recording method if there is already a “plus”?
In principle, in this case, in terms of convenience of notation, “5 x 2” differs little from “5 + 5”. But what if 5 sheets of paper had to be distributed to 10 children?
Then you would have to write down 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 50. And if you would need to distribute 5 sheets to the whole class? It would not be very convenient to write this down using addition. So, if you need to distribute five sheets of paper to ten children, using the multiplication sign, this can be written briefly:
5 x 10 = 50. But let's get back to the main topic for now.
Ways to write a multiplication table by 2:
| x | raised point | * | Sign not specified |
|---|---|---|---|
| 1 x 2 = 2 | 1 ∙ 2 = 2 | 1 * 2 = 2 | 1 __ 2 = 2 |
| 2 x 2 = 4 | 2 ∙ 2 = 4 | 2 * 2 = 4 | 2 __ 2 = 4 |
| 3 x 2 = 6 | 3 ∙ 2 = 6 | 3 * 2 = 6 | 3 __ 2 = 6 |
| 4 x 2 = 8 | 4 ∙ 2 = 8 | 4 * 2 = 8 | 4 __ 2 = 8 |
| 5 x 2 = 10 | 5 ∙ 2 = 10 | 5 * 2 = 10 | 5 __ 2 = 10 |
| 6 x 2 = 12 | 6 ∙ 2 = 12 | 6 * 2 = 12 | 6 __ 2 = 12 |
| 7 x 2 = 14 | 7 ∙ 2 = 14 | 7 * 2 = 14 | 7 __ 2 = 14 |
| 8 x 2 = 16 | 8 ∙ 2 = 16 | 8 * 2 = 16 | 8 __ 2 = 16 |
| 9 x 2 = 18 | 9 ∙ 2 = 18 | 9 * 2 = 18 | 9 __ 2 = 18 |
| 10 x 2 = 20 | 10 ∙ 2 = 20 | 10 * 2 = 20 | 10 __ 2 = 20 |
Ways to write a division-by-2 table:
| / | : | ÷ | Unsigned |
|---|---|---|---|
| 2 / 2 = 1 | 2: 2 = 1 | 2 ÷ 2 = 1 | 2 __ 2 = 1 |
| 4 / 2 = 2 | 4: 2 = 2 | 4 ÷ 2 = 2 | 4 __ 2 = 2 |
| 6 / 2 = 3 | 6: 2 = 3 | 6 ÷ 2 = 3 | 6 __ 2 = 3 |
| 8 / 2 = 4 | 8: 2 = 4 | 8 ÷ 2 = 4 | 8 __ 2 = 4 |
| 10 / 2 = 5 | 10: 2 = 5 | 10 ÷ 2 = 5 | 10 __ 2 = 5 |
| 12 / 2 = 6 | 12: 2 = 6 | 12 ÷ 2 = 6 | 12 __ 2 = 6 |
| 14 / 2 = 7 | 14: 2 = 7 | 14 ÷ 2 = 7 | 14 __ 2 = 7 |
| 16 / 2 = 8 | 16: 2 = 8 | 16 ÷ 2 = 8 | 16 __ 2 = 8 |
| 18 / 2 = 9 | 18: 2 = 9 | 18 ÷ 2 = 9 | 18 __ 2 = 9 |
| 20 / 2 = 10 | 20: 2 = 10 | 20 ÷ 2 = 10 | 20 __ 2 = 10 |
